Bulletin of the
Korean Mathematical Society BKMS

In this paper, we prove some existence and uniqueness results on coincidence points for $g$-monotone mappings satisfying linear as well as generalized nonlinear contractivity conditions in ordered metric spaces. Our results generalize and extend two classical and well known results due to Ran and Reurings (Proc. Amer. Math. Soc. {\bf 132} (2004), no. 5, 1435--1443) and Nieto and Rodr\'{\i}guez-L\'{o}pez (Acta Math. Sin. {\bf 23} (2007), no. 12, 2205--2212) besides similar other ones. Finally, as an application of one of our newly proved results, we establish the existence and uniqueness of solution of a first order periodic boundary value problem.

Keywords: ordered metric space, TCC property, termwise monotone sequence, c-bound

MSC numbers: 47H10, 54H25